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<p> Observing the non-equilibrium dynamics of the invisible ultrafast atomic and sub atomic world requires optical tools with ultrashort bursts of light and wavelengths. Such optical sources can provide us with the ultimate understanding of the quantum universe in the 4D space-time continuum at femto-zeptosecond time and nano-picometer spatial scale. Revealing at the same time, the 'extra dimensions' of the chemical nature of matter with elemental specificity, e.g., oxidation, charge/spin localization to specific elements, etc. To expand the frontiers of knowledge, there is a simple solution: coherent ultrafast X-ray or gamma&ndash;ray laser light. Amongst the numerous X-ray light sources that exist or have been developed to date, there are just two practical complementary alternatives: giant free electron X-ray laser facilities and compact high harmonic generation X-ray lasers. This thesis focuses on the latter. </p><p> High harmonics result from the extreme nonlinear response of matter to strong laser fields. However, due to inability to phase match, the available bright HHG sources were limited to the EUV spectral region ~0.15<i> keV.</i> We report on two routes for efficiently obtaini bright, coherent X-ray light. The first approach, takes advantage of the ultra-high emission per atom and ion species, the large refractive indices, and small phase mismatch, using high intensity UV lasers. Here the specifics of the phase matching and group velocity matching lead to bright soft X-ray emission from ions and atoms, even at ionization levels above 500%. Using UV light at 0.270<i>&micro;m, </i> the harmonics extend above 280<i>eV</i> while the expec phasematching cutoff was believed to be 23<i>eV</i>. Second, using IR lasers, where the process o phase matching favors the coherent buildup of X-rays from many atomic emitters at high gas density over long distances at extremely low ionization levels. The X-rays supercontinua driven by Mid-IR light at &lambda;_L = 3.9<i>&micro;m,</i> extends over ~12 octaves to > 1.6<i>keV,</i> and broadest spectrum generated to date from any small or large source. Calculations indicate that we can extend further the emission to the hard X-ray region and beyond using high laser intensity UV-EUV lasers or low intensities IR-Far IR lasers, without significantly sacrificing the X-ray flux. However, special highly transmissive fibers are required for phase matching in the Mid-IR region, where the propagation distances are longer than the self-guiding lengths. In addition, the flux from the Mid-IR driven HHG is expected to decrease substantially or cease due to a large <i>v</i> vector &times; <i>B</i> vector drift of the returning electrons caused by th magnetic field <i> B</i> vector and because of the large quantum diffusion of the electron wavepacket. We propose and design special photonic bandgap waveguides to resolve all the issues limiting the flux of IR and Mid-IR and UV driven hard X-rays. </p><p> The properties of the X-rays, driven by UV and IR lasers, are completely contrasting: supercontinuum versus isolated sharply peaked harmonics, we predict chirped isolated single pulses on sub or femtosecond scale as opposed to near transform limited train of attosecond pulses, respectively for IR and UV-driven harmonics. While pressure phase matching has been widely used we introduce the concept of pressure-temperature tuned phase matching for the process of HHG generation that additionally increases the flux. </p><p> Moreover, we report on harmonic generation with extremely high flux at near <i>mW</i> and <i>&micro;J</i> level, that allows us to perform experiments, which were previously only possible in large-scale facilities. While a magnetic scattering cross section is orders of magnitude smaller than the charge scattering cross section, we demonstrate resonant magnetic ptychography coherent diffraction imaging at the <i>Fe, M</i>-edge, using narrow bandwidth X-rays light, to lo at buried magnetic domain structure. Using broad 'water window' and keV coherent X-ray supercontinua, we extract atomic structure on picometer spatial resolution and chemical bonds' information, through x-ray absorption spectroscopy measurements at various absorption edges. </p><p> Such unique light tools will make it possible to answer even questions that have not yet been asked or may have never been imagined.</p><p>

Alzheimer’s disease (AD), the most prevalent neurodegenerative disease, is characterized in part by disruptions in axonal transport. Axonal transport is a process by which motor proteins carry organelles and other cargo made in the neuronal cell body along microtubule tracks to distal regions of the axon. The microtubule-associated protein (MAP) Tau plays a crucial role in regulating axonal transport, and is implicated in the development of AD and other types of dementia collectively known as Tauopathies. Tau is a neuronal-specific MAP that has six isoforms alternatively spliced from a single gene. These isoforms differ by the presence of zero, one, or two N-terminal acidic inserts and three or four C-terminal microtubule binding repeats. Tau is also known to be an intrinsically disordered protein that undergoes a dynamic equilibrium between static and diffusive states on the microtubule surface. The dynamics of Tau are important in the regulation of motor protein mediated axonal transport in neurons. Isoform-specific differences in the dynamic behavior of Tau on the microtubule surface, however, are not yet fully understood. Diffusive Tau is thought to be stabilized by electrostatic interactions between its N- and C-termini while static Tau is proposed to be extended with its C-terminal repeats contacting the microtubule and the N-terminus projected away from the microtubule surface. Thus, the N-terminal inserts may help regulate Tau’s dynamic behavior and function during axonal transport. In this study, the dynamics of two different isoforms of Tau, both with three-microtubule binding repeats but a different number of N-terminal acidic inserts, were assessed using single molecule imaging techniques and novel data analysis methods.

In this study, Amsterdam Density Functional software is used to model bimetallic and ligated aluminum clusters. The stability of the bimetallic clusters is well described by the Jellium model, and the nature of bonding between dopants and aluminum in the bimetallic clusters is analyzed using different criteria. We find that sodium tends to bind ionically, while the bonding of magnesium is not so obvious. We also determine that examining the Mulliken population is the most useful parameter in differentiating bonding character. Calculations on ligated aluminum clusters reveal it behaves fundamentally different than the bimetallic clusters studied in the first part. The ligated clusters contained a high HOMO-LUMO gap regardless of size and the aluminum showed a high 3p Mulliken population. These results show ligated aluminum clusters behave according to Wade-Mingos counting rules.

A systematic investigation is carried out of the multiplicity of potential energy minima for up to 13 atoms interacting under central two-body potentials of Lennard-Jones and Morse type. The sets of minima discovered by various growth algorithms are believed to be virtually exhaustive of all possible N-atom isomers for the potentials used, with N 14. These are classified according to the presence of crystallographic or non-crystallograpnic (5-fold) symmetry, and their energy distributions are statistically analyzed. It is shown that non-crystallographic configurations predominate in structures of both greatest and least binding energy. A striking result is the extreme sensitivity of the number of possible stable minima tovariations in the range and softness of the pair potential. Thus, of no fewer than 988 energetically distinct minima for 13 Lennard-Jones (6-12) atoms, only some 36 are supported by the Morse (a = 3) potential. A vibrational analysis is performed for each configuration and the resulting vibrational frequencies are used to construct an approximation to the multi-configuration partition function (MCPF). This partition function is compared with the corresponding single-configuration partition function derived from the most stable cluster (SCPF) . Tnermodynamic properties for monatomic systems of rare gases, based on a rigid rotor/harmonic oscillator (RRHO) approach, are obtained via both single- and multi-configuration partition functions. It is seen that the validity of the single-configuration approximation depends strongly upon the distribution of isomer energies and less strongly upon the number of these isomers. From the computed partition functions equilibrium constants and relative concentrations are estimated, asis the size of the critical nucleus at various pressures. The first five reduced virial coefficients are calculated and a correspondence between the equilibrium constants and Mayer's Cluster Integrals presented. The use of graph theory in the enumeration of geometrically distinct isomers in 3 and higher dimensional spaces is noted, and adjacency matrices for some specific isomers constructed. Inspection of these matrices enables one to determine how compact the corresponding structures are.

This thesis is concerned with the study of the excitation of Hydrogen atoms to the n = 3 states from the ground state by electrons with incident energies ranging from just above the ionization threshold to energies where the first Born approximation is expected to be valid. The major physical effects in this region are exchange, the distortion of the wave describing the external electron, and the distortion of the atomic system. A model which includes these effects - the Distorted Wave Polarized Orbital (DWPO) approximation - is generalized for any excitation and used to investigate the excitation process for n = 3 in particular. Total (integrated) and differential cross sections, not previously calculated using this model, are presented and compared, where possible, with other theoretical and experimental work. Other sensitive indicators of the effects of the model are considered. These include the polarization of Balmer-a (Ha) radiation and the parameters which describe the orientation and alignment of the atomic system after collision and the coincidence rate for the observation of emitted photons with the ejected electrons (Fano-Macek and Macek-Jaecks parameters). Also studied is the asymmetry in the observed intensity of Ha radiation arising on sign reversal of an applied electric field along the interaction direction. There is a serious disparity between the results in this model or the Born approximation and the experimental observations. A number of reasons for this are discussed. The work here indicates a need for further theoretical and experimental study but that high levels of sensitivity are required in any experimental work particularly with regard to the polarization and asymmetry measurements. Addition any, this work illustrates a very serious failure in the DWPO model caused by the use of the adiabatic polarization potential rather than an energy dependent potential especially at higher energies in the 3d excitation where we found that for the total cross section, the results obtained by including full allowance for polarizationlie a factor of about 2.5 below the Bom result at 200 eV and do not approach the Born cross section even for impact energies measuredin keV. The most useful line of future research is expected to be the allowance for coupling to adjacent states by the unitarizaticn method and some preliminary work for this is included.

This thesis is concerned with a study of inelastic electron-atom collisions with the incident energy ranging from just above the first ionization threshold to some energy where the First Born approximation becomes valid. The main physical effects which need to be included in the theoretical treatment of such collisions are electron exchange and distortion of both the atomic system and the wave describing the external electron. A method which takes account of these effects, to be referred to as the Distorted Wave Polarized Orbital (DWPO) approximation, is described. Three models based on this approximation are developed and applied to electron collisions with the light atoms hydrogen and helium. In particular the models are applied to the following collision processes: e + H(ls) &rarr; e + H(2s, 2p, 2s + 2p); e + He(11S) &rarr; e+ He(n1,3L), n = 2,3,4,5, L= S,P. Results are presented for the total (integral)and differential cross sections and also, where appropriate, for the parameters describing the orientation and alignment properties of the excited atom. The results are compared with those of other theoretical methods and with experimental measurements.

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